David Cameron could not have put it more clearly in his conference speech last week: Britain has reached its hour of reckoning, when we either do or decline. He promised to slay the three modern “giants” holding this country back – the debt strangling our economy, welfare dependency, and the educational mediocrity that prevents so many young people from flourishing. Of these challenges, none is more important to the fulfilment of our common potential than sorting out the chronic weakness that affects England’s schools.

Consider these facts: in 40 per cent of schools teaching is no better than satisfactory, and 6,000 schools provide only a satisfactory level of education. Earlier this year Sir Michael Wilshaw, the chief inspector of schools and an outstanding headteacher in his day, confirmed what everyone knew – that “satisfactory” in education is anything but. It is now clear that the problems run much deeper than we thought. So what can this Government do about it?

The first piece of good news is that the academy programme is working. According to both the National Audit Office and the London School of Economics, failing schools that have been turned into academies under new sponsors are performing better than those that did not. So the expansion of the academies programme will help raise standards, as will the influence of innovative new free schools. But ultimately this policy was designed to turn round a few hundred schools, not for helping the thousands of schools that now need to improve.

Michael Gove, the Education Secretary, needs more ways to raise standards, so he should take advantage of an even more effective form of educational organisation that has emerged over the past 10 years – federations or chains of academies. Chains are charitable groups of schools with a single educational vision, bound together legally, financially and operationally. They work by spreading the benefits of a successful approach to schooling: a “no excuses” culture, strong leadership, high expectations and robust discipline.

The emerging evidence suggests that, on average, their standards are even higher than single academies because they provide exactly the kind of opportunities for collaboration, within a competitive marketplace, that schools need to flourish. Chains show that a proper market in state schooling is at last starting to develop.

Academy chains have many different roots. Some of the original academy sponsors like the United Learning Trust have come from the independent sector and are now running several academies. I am currently working with Wellington College to create a chain, and academy chains based around successful state schools or colleges can now be found across the country: the Kemnal Academies Trust on the South Coast, the Harris Federation in London, and the Barnfield Federation in Luton. Others, such as ARK Schools, were started by philanthropists.

We need to harness the power of these academy chains to deal with what the Prime Minister has called the “hidden crisis” of coasting schools. That means encouraging the creation and growth of chains – by part-funding their expansion and giving the best chains more influence by making them centres of teacher training – as well as giving them opportunities to innovate, such as by paying their governing bodies. It means explicitly using them to sort out failure. If turning a weak school into a stand-alone academy fails to improve results, then that school should be handed over to a successful chain. We also need to create a network of local school commissioners who, under the direction of central government, will intervene in the thousands of underperforming schools and turn them over to an academy sponsor or successful chain.

These changes can take us a long way, but the scale of the challenge is so big that even dramatically increasing the number and size of academy chains may not be enough. This is where the private sector should be asked to contribute. If turning a school into an academy and then handing it on to a chain haven’t been enough to break the cycle of underachievement, the governing body should be obliged to appoint an external provider to run it. The school and its assets would stay in the charitable sector, but they would be able to access the expertise of private providers who would be paid by results. Any objections to the private sector trying where the state and voluntary sectors have failed should be dismissed for what they are – ideological prejudice. There are countless examples of the private sector delivering excellent services to citizens across the public sector, from the NHS to special educational needs provision. Mainstream schooling should be no different.

The consequences I am proposing for underperforming schools are robust; they will not be universally popular. But as Sir Michael Wilshaw has said: “We have tolerated mediocrity for too long… Without radical change now, we will see more social and economic division in this country.” There is no time to waste. Creating a world-class education system means calling on the best chains, independent schools and private providers to raise standards in the weakest schools. It is time to sink or swim.

James O’Shaughnessy is a former head of policy at No 10 Downing Street. 'Collaboration meets Competition’ is published today by Policy Exchange